Mappings which preserve regular dodecahedrons.
Menger curvature and Lipschitz parametrizations in metric spaces
We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.
Metric criteria for Banach and Euclidean spaces
Necessary and sufficient conditions for unique determination of plane domains.
Nonlinear orthogonal projection
We discuss some properties of an orthogonal projection onto a subset of a Euclidean space. The special stress is laid on projection's regularity and characterization of the interior of its domain.
On four-colourings of the rational four-space.
On Lorentz-Minkowski geometry in real inner product spaces.
On metric products
On moduli of expansion of the duality mapping of smooth Banach spaces.
On pairs of metrics invariant under a cocompact action of a group.
On the -angle and -angle in normed spaces.
On the interpoint distance sum inequality.
On the iso-taxicab trigonometry.
On the ordered sets in -dimensional real inner product spaces.
On the plane geometry with generalized absolute value metric.
On the tangency of sets in generalized metric spaces for certain functions of the class
On -distance in three dimensional space.
Problems of Distance Geometry and Convex Properties of Quadratic Maps.
Producto, convexificación y completación de espacios métricos generalizados y probabilísticos.
En 1967 E. Trillas introdujo la noción de espacio métrico generalizado, al considerar métricas abstractas valoradas en semigrupos ordenados, unificando con este punto de vista algebraico-reticular las estructuras métricas reales de M. Fréchet ([5]) y los espacios métricos probabilísticos de K. Menger ([6]) (así como los espacios Booleanos de Blumenthal ([4]) y las métricas naturales definidas en grupos ordenados). En el presente artículo se abordan los problemas de la topología del orden, del producto,...
Proximinality in geodesic spaces.